What sum of money will earn an interest of `₹160` at the rate of `4%` per year for `2` years ?

Answer

To find the sum of money (P) that will earn an interest of ₹160 at the rate of 4% per year for 2 years, we can use the formula for Simple Interest (SI):

### Step 1: Write down the formula for Simple Interest
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount (the sum of money we need to find)
- \(R\) = Rate of interest per year
- \(T\) = Time in years

### Step 2: Substitute the known values into the formula
We know:
- \(SI = 160\)
- \(R = 4\%\)
- \(T = 2\) years

Substituting these values into the formula gives:
\[ 160 = \frac{P \times 4 \times 2}{100} \]

### Step 3: Simplify the equation
First, calculate \(4 \times 2\):
\[ 4 \times 2 = 8 \]
Now substitute back into the equation:
\[ 160 = \frac{P \times 8}{100} \]

### Step 4: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 100:
\[ 160 \times 100 = P \times 8 \]
This simplifies to:
\[ 16000 = P \times 8 \]

### Step 5: Solve for P
Now, divide both sides by 8 to find \(P\):
\[ P = \frac{16000}{8} \]
Calculating the division gives:
\[ P = 2000 \]

### Conclusion
The sum of money that will earn an interest of ₹160 at the rate of 4% per year for 2 years is **₹2000**.

---